The dates on this coin don't seem to match. L'an 5 should have been 1796,
not 1793. Also, Louis was executed January 21, 1793. It seems likely that
the obverse was used until it broke. There is a serious flaw completely
through Louis' bust, the bust is also very smooth, as if it had been changed
to eradicate his features. Perhaps there was a lack of sculptors.

"I think I can solve the problem on the dates here. After the Revolution,
the French experimented more than once with the calendar. Firstly came the
French Constitutional Calendar which counted the years from the storming
of the Bastille, i.e. 14th July 1789. These were known as Years of Liberty
(Les Ans de la Liberté). These years ran concurrently with the years
of the traditional calendar (the first year was a short one running from
14th July 1789 to 31st December 1789). Year 5 of Liberty, the final year
of this calendar, ran therefore from 1st January 1793 to 31st December 1793,
and this is the year in which your 2 sols coin was produced (the reverse
date clearly states L'An 5 de la Liberté). The French Calendar of
the Republic did not begin until 22nd September 1792 and therefore slightly
overlapped the earlier Constitutional Calendar.

The flaw through the centre of the obverse is interesting though I am
not sure it was caused by a cracked or broken die. Die cracks usually start
at the edge of a die and gradually work their way across the surface as
the die receives continued use. In this case, the edges of the coin do not
appear to show any die damage, the flaw confining itself to the king's bust.
I would think that corrosion of some sort is more likely. As far as the
smoothness of the king's bust is concerned, I have a few worn copper pieces
of this era and have noted that the rather shallow relief on the original
image does wear away quite readily leaving the smoothness you describe."

Thanks to Mish Webster for the info!

Very informative! It still leaves me with a couple of questions but that's
part of the fun of all this. The smoothness I mentioned before appears deliberate,
almost polished. Notice that the surrounding coin is nearly flawless. Also,
thanks for the info on the Years of Liberty. Since Louis XVI lost his head
in January of L'An 5 this may be another reason that the bust appears to
be deliberately smoothed. Hm...